Super Modified Combination Sum

Algebra Level 3

\[ \large\displaystyle \sum_{k=1}^{504} \left ( 4k-1 \right ) \binom{2015}{4k-1} \]

If the sum above can be written as \( p.q^{r} \), where \(p\), \(q\) and \(r\) are positive integers with \(q\) being a prime.

Evaluate \( p+q+r \).

Image Credit: Wikimedia TED-43.
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